Geodesic
Semiregular automorphisms of edge-transitive graphs
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 4, pp. 961-972.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The polycirculant conjecture asserts that every vertex-transitive digraph has a semiregular automorphism: a non-trivial automorphism whose cycles all have the same length. In this paper, we investigate the existence of semiregular automorphisms of edge-transitive graphs. In particular, we show that any regular edge-transitive graph of valency three or four has a semiregular automorphism.
Classification : 05C20, 05C60, 05C25
Keywords: edge-transitive graphs, semiregular automorphism, polycirculant conjecture 
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Giudici, Michael; Potočnik, Primož; Verret, Gabriel. Semiregular automorphisms of edge-transitive graphs. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 4, pp. 961-972. http://geodesic.mathdoc.fr/item/JAC_2014__40_4_a7/